Question 408081: 6. Each day a quality engineer selects a random sample of 100 bolts from the day’s production, measures their lengths, and computes a 95% confidence interval for the mean length of all the bolts manufactured that day. What is the probability that more than 15 of the confidence intervals constructed in the next 250 days will fail to cover the true mean?
7. On a certain day, a large number of fuses were manufactured, each rated at 15A. A sample of 75 fuses is drawn from the day’s production, and 17 of them were found to have burnout amperages greater than 15A.
a. Find a 95% confidence interval for the proportion of fuses manufactured that day whose burnout amperage is greater than 15A.
b. Find a 98% confidence interval for the proportion of fuses manufactured that day whose burnout amperage is greater than 15A.
c. Find the sample size needed for a 95% confidence interval to specify the proportion to within ±0.05
d. Find the sample size needed for a 98% confidence interval to specify the proportion to within ±0.05
e. If a 95% confidence interval is computed each day for 200 days, what is the probability that more than 192 of the confidence intervals cover the true proportions?
8. A random sample of 400 electronic components manufactured by a certain process are tested, and 30 are found to be defective.
a. Let p represent the proportion of components manufactured by this process that are defective. Find a 95% confidence interval for p.
b. How many components must be sampled so that the 95% confidence interval will specify the proportion defective to within ±0.02?
9. A chemist made 8 independent measurements of the melting point of tungsten. She obtained a sample mean of 3410.14oC and a sample standard deviation of 1.018oC.
a. Find a 95% confidence interval for the melting point of tungsten
b. Find a 99% confidence interval for the melting point of tungsten
c. If the eight measurements had been 3409.76, 3409.80, 3412.66, 3409.79, 3409.76, 3409.77, 3409.80, and 3409.78, would the confidence intervals found in parts (a) and (b) be valid? Explain.
Answer by solver91311(24713)   (Show Source):
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